Basic properties
Modulus: | \(2058\) | |
Conductor: | \(343\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(147\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{343}(65,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2058.u
\(\chi_{2058}(25,\cdot)\) \(\chi_{2058}(37,\cdot)\) \(\chi_{2058}(109,\cdot)\) \(\chi_{2058}(121,\cdot)\) \(\chi_{2058}(151,\cdot)\) \(\chi_{2058}(163,\cdot)\) \(\chi_{2058}(193,\cdot)\) \(\chi_{2058}(205,\cdot)\) \(\chi_{2058}(235,\cdot)\) \(\chi_{2058}(247,\cdot)\) \(\chi_{2058}(277,\cdot)\) \(\chi_{2058}(289,\cdot)\) \(\chi_{2058}(319,\cdot)\) \(\chi_{2058}(331,\cdot)\) \(\chi_{2058}(403,\cdot)\) \(\chi_{2058}(415,\cdot)\) \(\chi_{2058}(445,\cdot)\) \(\chi_{2058}(457,\cdot)\) \(\chi_{2058}(487,\cdot)\) \(\chi_{2058}(499,\cdot)\) \(\chi_{2058}(529,\cdot)\) \(\chi_{2058}(541,\cdot)\) \(\chi_{2058}(571,\cdot)\) \(\chi_{2058}(583,\cdot)\) \(\chi_{2058}(613,\cdot)\) \(\chi_{2058}(625,\cdot)\) \(\chi_{2058}(697,\cdot)\) \(\chi_{2058}(709,\cdot)\) \(\chi_{2058}(739,\cdot)\) \(\chi_{2058}(751,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{147})$ |
Fixed field: | Number field defined by a degree 147 polynomial (not computed) |
Values on generators
\((1373,1375)\) → \((1,e\left(\frac{10}{147}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 2058 }(751, a) \) | \(1\) | \(1\) | \(e\left(\frac{143}{147}\right)\) | \(e\left(\frac{22}{147}\right)\) | \(e\left(\frac{19}{49}\right)\) | \(e\left(\frac{103}{147}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{23}{147}\right)\) | \(e\left(\frac{139}{147}\right)\) | \(e\left(\frac{25}{49}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{5}{147}\right)\) |